My TV is advertised as 1080p and only does 1320x768. As long as it's above 720p they can claim 1080p. It seems that your actual question is whether it's the TV or your computer/connection. It's your TV, the resolution you're getting is its maximum resolution. The maximum resolution HDMI can do is generally 1080p (1920x1080).
This is technically not true, since HDMI can do pretty much any resolution DVI can do, but since it's a multimedia interface 1080p is likely the highest resolution a display you can connect via HDMI will give you (for now, at least).